# ARAAC: A Rational Allocation Approach in Cloud Data Center Networks

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## Abstract

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## 1. Introduction and Problem Statement

- Allocating the network resources on the basis of the market clearing price may help the cloud-DCN provider avoid losses, however, it can never achieve profit maximization. Indeed, knowing that the offered bid prices will not be considered for the charging issues, bidders will always tend to offer high bid prices simply to win the auction. Then all those who win the auction pay the same price defined by that market clearing price.
- The absence of a competition environment in such an allocation scenario can motivate exaggeration actions. Bidders with no incentives to truthfully reveal their true needs and real resource requirements, may tend to exaggerate their needs and ask for more resources. Living with such huge growth in the global network traffic, exaggerated actions may impose real waste for the available cloud resources.
- Cutting portions from the requested network resources contradicts the tenants’ satisfaction goals. In truth, those bidders who receive only portions of what they have asked for may not be satisfied as this may affect their QoS requirements.

- ARAAC provides for strategy-proofness [5] and an incentive-compatible [6] solution that encourages truthful reveals for the required cloud-DCN resources, thus leading to high utilization rates. This comes through the competition environment enforced throughout the SBP [7] and the behavior-based reputation mechanisms.
- ARAAC allows for a fair allocation model that motivates the tenants’ positive behaviour, while it does not affect their required service levels. Fairness comes from the fact that ARRAC allocates the resources to those bidders with positive behavior and competing offered prices.
- ARAAC motivates reasonable bid prices that maximizes the cloud-DCN providers profits while not being a greedy allocation approach [8]. ARAAC chooses the winning bidders not only through their offered bid prices, but according to their usages’ behavior.

## 2. ARAAC: A Rational Allocation Approach in Cloud-Service Networks

#### 2.1. Definitions and Mathematical Modeling

**Definition 1:**(Provider’s Utility.) The utility of the cloud-DCN provider in such a game is represented in the charges collected from the cooperative tenants nominated for allocation. In ARAAC, this is calculated as shown in Equation (1), which adds the different charges collected per accepted request i, ∀i∈N:$$U}_{\mathrm{p}}=\sum _{i=1}^{N}{s}_{i}\xb7{{p}_{i}}^{*$$**constraints**:**Behavior-Based Threshold:**For each bidder i, an identification reference ${d}_{i}$ is used to link i to a database that collects information related to the bidder’s previous history, in regard to its resource utilization behavior ${e}_{i}$ throughout a certain time window predefined by the market providers. For bidder i to be listed among the candidates for allocation, its behavior score ${e}_{i}$ needs to pass the behavioral threshold value ${E}_{t}$. At each auction round t, the threshold value may be revised by the providers according to the market state. The formulation of this constraint is given by:$${e}_{i}\ge {E}_{t}\phantom{\rule{2.em}{0ex}};\forall i\in N$$**Leasing Price-unit Threshold:**For each bidder i, to be considered for allocation among the set of candidates, its offered price-unit ${p}_{i}$ needs to be higher than or at least equal a predefined price-unit threshold ${{P}^{\u2605}}_{t}$. The process of defining such threshold follows the providers’ profit objectives and market state at the allocation period t. With such threshold, ARAAC allows to maintain the providers’ profit objectives and avoids losses. Such constraint is given by:$${p}_{i}\ge {P}_{t}^{\u2605}\phantom{\rule{2.em}{0ex}};\forall i\in N$$**Resource Availability:**To control the allocation decision, those bidders who satisfy the aforementioned two constraints are sorted in N according to their offered price-units ${p}_{i}$. After having the bidders sorted, and according to their required resource units ${s}_{i}$, for each bidder i, the provider checks if it has sufficient resource capacities for allocation in accordance to the residual resources ${\alpha}_{t}{S}_{t}$ after previous allocations. At each auction round t, the cloud-DCN provider defines the portion ${\alpha}_{t}$ of the resources available for allocation ${S}_{t}$. Hence, each candidate bidder i needs to pass the following:$$\sum _{i=1}^{N}{s}_{i}\le {\alpha}_{t}{S}_{t}$$Those bidders who pass the aforementioned three constraints are stored in the candidate list C, and thus are charged for their granted services according to the pricing policy set by the cloud-DCN providers. In ARAAC, the model chooses the SBP policy to set the charges for its service tenants.**Definition 2:**(Tenants’ Utility.) The utility of the service-tenants (i.e., the bidders) in the allocation game is represented by the gain a tenant can collect from participating in the auction. Being a candidate for allocation, and besides the service granted by the allocation itself, the financial-utility is calculated in Equation (5) below as the difference between the sum of the offered price unit ${p}_{i}$ and the charged price ${{p}_{i}}^{*}$ for the required service resource units ${s}_{i}$. Intuitively, the objective for each tenant i is to maximize the value of ${U}_{i}$ given below:$${U}_{i}=\mathrm{max}\phantom{\rule{0.277778em}{0ex}}({\displaystyle \sum {p}_{i}-\sum {{p}_{i}}^{*}})$$The calculation of the tenants’ utility is also bounded by the constraint discussed next:**Partial Allocation is Not Accepted:**To ease the presentation of such constraint, we define ${s}_{i}$ as a set of entities referred to by ${s}_{{i}_{j}}$ where $j\in J$. It is worth to highlighting that allocation in this work is for service instances, and such instances require various types of network and computing resources. This includes resources such as bandwidth, switching capacities, memory space, and CPU cycles. Hence, the allocation of ${s}_{i}$ is met only when all the j entities are granted, otherwise the allocation is not considered. Such constraint is described by:$$\sum _{j\in J}{s}_{{i}_{j}}=1\phantom{\rule{2.em}{0ex}};{s}_{{i}_{j}}\in \{0,1\},i\in C$$**Definition 3:**(Incentive Compatible Approach). The proposal of ARAAC provides an incentive compatible [6] approach that motivates the rational service-tenants to reveal their truthful valuation of the required services (i.e., resource units). Indeed, bids with low price units ${p}_{i}$ may be excluded from the auction, as they do not satisfy a predefined price-unit threshold ${P}^{\u2605}$, while others with reasonable offered price units are rewarded by having the required resources allocated, and only pay the next highest price (i.e., the SBP in row). This allows for positive utilities. Moreover, ARAAC also motivates efficient resource utilization. True, bidders with bad utilization behavior records ${e}_{i}$ may find themselves deprived of being candidates for allocation in this round and others, regardless of their offered prices units.**Definition 4:**(Individual Rationality [10]). ARAAC can be considered as an approach that provides for rational allocation. Regardless of the offered price-units, it excludes those bidders with low reputation records, and instead, it allows others with potentially lower offered prices for allocation, as they have attained certain levels of reputation. Accordingly, we can clearly state that ARAAC maximizes the providers’ profits while not being greedy. Indeed, among the bids with high offered price units, only those with acceptable reputation records remain; others are excluded regardless of their offered bids.

#### 2.2. ARAAC’s Allocation Algorithm

**id**entification reference ${d}_{i}$ (used to link with a reputation database), (2) its required

**s**ervice ${s}_{i}$ (i.e., resource units), and (3) its offered

**p**rice-unit ${p}_{i}$. Having the aforementioned three pieces of information, the model follows the algorithm presented in Table 1 to choose the candidate bidders for allocation.

#### 2.3. Benchmark Mechanisms

#### 2.3.1. SBP: Second Best Price

#### 2.3.2. Tit-for-Tat & Second-Best Price

## 3. Simulation Results

#### 3.1. Service and Tenant Instances

#### 3.2. Discussion

## 4. Related Work

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Allocation Algorithm: Selecting the Candidate Service Tenants for Allocation |
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1: Input: Vector of offered bids N, ∀ i ∈ N, collect (${d}_{i}$, ${s}_{i}$, ${p}_{i}$); |

2: Output: Vector of candidate tenants for allocation C; |

3: for all i ∈ N; |

4: find the value ${p}_{i}$, then |

5: sort them accordingly in N as ${p}_{i}$ > ${p}_{i+1}$ > ${p}_{i+2}$ > ... > ${p}_{n-1}$ > ${p}_{n}$ ; |

6: update N; |

7: end |

8: for all i ∈ N; |

9: find the reputation record ${e}_{i}$ associated with the id ${d}_{i}$, then |

10: exclude all those who have ${e}_{i}$ < ${E}_{t}$; |

11: update N; |

12: end |

13: for all i ∈ N; |

14: if ${p}_{i}$ < ${{P}^{\u2605}}_{t}$, exclude from N; |

15: else keep in N; |

16: end |

17: for all i ∈ N; |

18: find bidder $\overline{i}$, where ${\sum}_{i=1}^{\overline{i}}$
(${s}_{i}\le {\alpha}_{t}{S}_{t}$) and ${\sum}_{i=1}^{\overline{i}+1}$ (${s}_{i}>{\alpha}_{t}{S}_{t}$); |

19: move bidders from i → $\overline{i}$ to a new vector C; |

20: end |

21: for each i ∈ C; |

22: choose ${p}_{i+1}$ as a cost-unit; |

23: choose ${{P}^{\u2605}}_{t}$ as a cost-unit for bidder $\overline{i}$; |

24: end |

Tit-for-Tat’s Algorithm: Selecting the Candidate Service Tenants for Allocation |
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1: Input: Vector of offered bids N, ∀ i ∈ N, collect (${d}_{i}$, ${s}_{i}$, ${p}_{i}$); |

2: Output: Vector of candidate tenants for allocation C; |

3: for all i ∈ N; |

4: find the value ${p}_{i}$, then |

5: sort them accordingly in N as ${p}_{i}$ > ${p}_{i+1}$ > ${p}_{i+2}$ > ... > ${p}_{n-1}$ > ${p}_{n}$ ; |

6: update N; |

7: end |

8: for all i ∈ N; |

9: find the reputation score ${l}_{i}$ associated with the id ${d}_{i}$, then |

10: exclude all those who have ${l}_{i}$ = 0; |

11: update N; |

12: end |

13: for all i ∈ N; |

14: find bidder $\overline{i}$, where ${\sum}_{i=1}^{\overline{i}}$
(${s}_{i}\le {\alpha}_{t}{S}_{t}$) and ${\sum}_{i=1}^{\overline{i}+1}$ (${s}_{i}>{\alpha}_{t}{S}_{t}$); |

15: move bidders from i → $\overline{i}$ to a new vector C; |

16: end |

17: for eachi ∈ C; |

18: choose ${p}_{i+1}$ as a cost-unit; |

19: end |

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**MDPI and ACS Style**

Quttoum, A.N.; Alsarhan, A.; Moh’d, A. ARAAC: A Rational Allocation Approach in Cloud Data Center Networks. *Future Internet* **2017**, *9*, 50.
https://doi.org/10.3390/fi9030050

**AMA Style**

Quttoum AN, Alsarhan A, Moh’d A. ARAAC: A Rational Allocation Approach in Cloud Data Center Networks. *Future Internet*. 2017; 9(3):50.
https://doi.org/10.3390/fi9030050

**Chicago/Turabian Style**

Quttoum, Ahmad Nahar, Ayoub Alsarhan, and Abidalrahman Moh’d. 2017. "ARAAC: A Rational Allocation Approach in Cloud Data Center Networks" *Future Internet* 9, no. 3: 50.
https://doi.org/10.3390/fi9030050